Turbine bucket shroud internal core profile

ABSTRACT

A turbine bucket including a bucket airfoil having a hollow tip shroud, the hollow tip shroud having a hollow core having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I, in inches, wherein the shape of the core is defined by the cloud of points listed which are distributed around each surface of the shroud, and the complete hollow portion of the tip shroud could be constructed by defining smooth sheet surfaces through the listed points.

BACKGROUND OF THE INVENTION

The present invention relates to turbine buckets having an airfoil and a tip shroud carried by the airfoil. More particularly, the invention relates to the internal core profile of a tip shroud carried by an airfoil of a turbine bucket. While the invention is intended in particular for a gas turbine, the use of a scaled design could be applicable to a steam turbine or aircraft engine.

Buckets for turbines typically comprise an airfoil, a platform, a shank and dovetail. The dovetail is secured in a complementary slot in a turbine wheel. Oftentimes, the airfoil includes an integrally formed tip shroud. The buckets including the airfoil and tip shroud are, of course, rotatable about the engine centerline during operation and the airfoil and the tip shroud are located in the hot gas path. Because the tip shroud is mounted at the tip of the airfoil, substantial stresses occur in the tip shroud fillet region between the tip shroud and the airfoil tip. Tip shrouds, whether hollow or solid, are typically designed to balance the mass distribution of the shroud around the top of the airfoil. A benefit of the hollow shroud is that it provides a shroud of reduced weight, but maintains considerable structural stiffness. This results in generally lower stresses in the airfoil-to-tip shroud fillet and improved creep life. Further, certain prior tip shrouds do not cover the airfoil throat, with resultant negative impact on stage efficiency due to flow leakage over the tip shroud.

BRIEF DESCRIPTION OF THE INVENTION

In accordance with an example embodiment of the present invention, there is provided an article of manufacture including a bucket airfoil having a hollow tip shroud, said hollow tip shroud having a hollow core having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I, in inches, wherein the shape of the core is defined by the cloud of points listed which are distributed around each surface of the shroud, and the complete hollow portion of the tip shroud could be constructed by defining smooth sheet surfaces through the listed points.

The invention may also be embodied in an article of manufacture including a bucket airfoil having a hollow tip shroud, said hollow tip shroud having a hollow core having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I, in a Cartesian coordinate system having its origin at a point A located 39.600 inches above the cold rotor center line at an intersection of the airfoil mean camber line and the leading-edge airfoil surface, its positive X axis defined by point A and a point B located 39.600 inches above the cold rotor center line at an intersection of the airfoil mean camber line and the trailing-edge airfoil surface, its positive X-Z plane defined by points A, B, and a point C located 49.862 inches above the cold rotor center line at an intersection of the airfoil mean camber line and the airfoil trailing-edge surface, and its Y axis defined using right-hand rule methodology, and wherein X, Y and Z are distances in inches, wherein the shape of the core is defined by the cloud of points listed which are distributed around each surface of the shroud, and the complete hollow portion of the tip shroud could be constructed by defining smooth sheet surfaces through the listed points.

The invention may further be embodied in an article of manufacture comprising a turbine wheel having a plurality of buckets, each of said buckets including an airfoil and a hollow tip shroud, said hollow tip shroud having a hollow core having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I, in inches, wherein the shape of the core is defined by the cloud of points listed which are distributed around each surface of the shroud, and the complete hollow portion of the tip shroud could be constructed by defining smooth sheet surfaces through the listed points.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other objects and advantages of this invention, will be more completely understood and appreciated by careful study of the following more detailed description of the presently preferred example embodiments of the invention taken in conjunction with the accompanying drawings, in which:

FIG. 1 is a schematic illustration of a turbine section having a second stage turbine bucket tip shroud having a pre-determined shroud core profile according to an example embodiment of the present invention;

FIG. 2 depicts a turbine blade with a full tip shroud;

FIG. 3 shows the blade of FIG. 2 with the top portion of the shroud removed along the section shown in FIG. 2 to reveal the interior cavity shape;

FIG. 4 is a plan view of the shroud of FIG. 2; and

FIG. 5 is another internal view of the shroud, this time cut along the section shown in FIG. 4.

FIG. 6 is a schematic perspective view of the turbine airfoil illustrating points used to determine the coordinate system used to determine the coordinates for the points set forth in Table 1; and

FIG. 7 is a perspective view also illustrating the coordinate system used to determine the coordinates for the points set forth in Table 1.

DETAILED DESCRIPTION OF THE INVENTION

Referring now to the drawing figures, particularly to FIG. 1, there is illustrated a hot gas path, generally designated 10, of a gas turbine 12 including a plurality of turbine stages. Three stages are illustrated. For example, the first stage comprises a plurality of circumferentially spaced nozzles 14 and buckets 16. The nozzles are circumferentially spaced one from the other and fixed about the axis of the rotor. The first stage buckets 16, of course, are mounted on the turbine rotor wheel 17. A second stage of the turbine 12 is also illustrated, including a plurality of circumferentially spaced nozzles 18 and a plurality of circumferentially spaced buckets 20 mounted on the rotor. The third stage is also illustrated including a plurality of circumferentially spaced nozzles 22 and buckets 24 mounted on the rotor 17. It will be appreciated that the nozzles and buckets lie in the hot gas path 10 of the turbine 12, the direction of flow of the hot gas through the hot gas path 10 being indicated by the arrow 26.

Each bucket 20 of the second stage is provided with a platform 30, a shank 32, and a dovetail 34 (FIG. 3) for connection with a complementary-shaped mating dovetail (not shown) on a rotor wheel forming part of the rotor 17. Each of the second stage buckets 20 also includes an airfoil 34 (FIG. 2) having an airfoil profile at any cross-section along the airfoil from the platform to the airfoil tip.

Each of the second stage buckets is provided with a tip shroud generally designated 36. The tip shrouds are preferably formed integrally with the airfoils 34 and each tip shroud 36 engages at circumferentially opposite ends adjacent tip shrouds of adjacent buckets to form a generally annular ring or shroud circumscribing the hot gas path at the axial location of the second stage buckets. The tip shroud 36 of each second stage bucket 20 includes first and second, leading and trailing, seal rails 42, 44 along its radial outer surface and which seal rails 42, 44 form nearly continuous seal rings about the tip shroud for sealing with the shroud 46 (FIG. 1) fixed to the turbine casing. In this regard, in an example embodiment, the forward seal rail 42 does not contact the corresponding seal rail on the adjacent bucket, but the aft seal rail 44 does in fact contact the corresponding seal rail on the adjacent bucket.

Turbine blades operate in a harsh environment due to thermal and mechanical loading. Furthermore, blades that have a tip shroud have additional challenges. Tip shrouds reside at the outermost extent of a blade, see FIG. 1, thus encountering high mechanical loading due to the rotational speed. It is therefore difficult to attach a non-scalloped shroud to a blade. Compounding this is the requirement that the blade's weight not exceed some maximum value. These constraints point to the benefit of a hollow turbine shroud.

To define the envelope or volume in which the core design of the invention resides, there is a unique set or loci of points in space. The loci which define the envelope or volume in which the core design resides comprises a set of 789 points with X, Y and Z coordinates relative to the origin coordinate system established as shown in FIGS. 6 and 7. More specifically, the coordinate system is set relative to the airfoil and is fully defined by points A, B and C. Points A and B are both located 39.600 inches above the cold rotor center line. Point A lies at the intersection of the airfoil mean camber line and the leading-edge airfoil surface. Point B lies at the intersection of the airfoil mean camber line and the trailing-edge airfoil surface. Point C is located 49.862 inches above the cold rotor center line and lies at the intersection of the airfoil mean camber line and the airfoil trailing-edge surface. The coordinate system origin is located at point A. Points A and B define the positive X axis. Points A, B and C define the positive X-Z plane. The Y axis is then defined using the right-hand rule methodology.

The Cartesian coordinate system of X, Y and Z values given in Table I below defines the complete hollow portion of the tip shroud. More specifically, the shape of the core is defined by the cloud of points listed which are distributed around each surface of the shroud, and the complete hollow portion of the tip shroud could be constructed by defining smooth sheet surfaces through the listed points. The coordinate values for the X, Y and Z coordinates are set forth in inches in Table I although other units of dimensions may be used if the values are appropriately converted.

The Table I values are generated and shown to 3 decimal places for determining the profile of the shroud core. These points represent the nominal cold or room temperature shape of the shroud core. As the bucket heats up in service, mechanical loading and temperature will cause a change in X, Y and Z's. Accordingly, values for the profile given in Table I represent ambient, non-operating or non-hot conditions.

There are typical manufacturing and coating tolerances which must be accounted for in the actual profile of the shroud core. It will therefore be appreciated that +/− typical manufacturing tolerances, i.e., +/− values, including any coating thickness are additive to the X and Y values given in Table I below. Accordingly, a distance of +/−0.042 inches in a direction normal to any surface location along the shroud core profile defines a shroud core profile envelope for this particular bucket tip shroud design and turbine, i.e., a variation between measured points on the actual shroud core surface at nominal cold or room temperature and the ideal position of these points as given in the Table below at the same temperature. The bucket shroud core design is robust to this range of variation without impairment of mechanical functions.

TABLE 1 X Y Z 0.320 2.170 10.700 0.462 2.174 10.704 0.373 2.132 10.707 0.703 2.125 10.709 0.551 2.216 10.710 0.344 2.119 10.710 0.293 2.228 10.712 0.792 2.167 10.713 0.854 2.035 10.720 0.640 2.258 10.721 0.943 2.077 10.722 0.310 2.265 10.725 1.006 1.945 10.734 1.095 1.987 10.738 0.400 2.307 10.738 0.262 2.294 10.740 1.157 1.855 10.745 0.489 2.350 10.750 0.614 2.085 10.753 1.247 1.897 10.756 0.360 2.087 10.757 0.228 2.368 10.758 0.881 2.211 10.758 1.309 1.765 10.761 0.248 2.399 10.762 1.033 2.121 10.769 0.730 2.302 10.770 0.337 2.441 10.772 1.371 1.633 10.773 0.187 2.455 10.774 0.765 1.995 10.775 1.460 1.675 10.777 1.398 1.807 10.778 0.327 2.157 10.782 1.220 1.723 10.782 1.523 1.543 10.789 0.917 1.905 10.791 1.068 1.814 10.791 0.578 2.393 10.792 1.612 1.585 10.797 0.186 2.532 10.799 1.184 2.031 10.799 0.427 2.484 10.802 0.150 2.535 10.808 1.550 1.718 10.809 0.275 2.575 10.813 0.287 2.245 10.815 0.800 1.695 10.987 0.329 2.930 10.990 −0.370 3.259 10.990 0.952 1.604 10.990 2.129 1.187 10.991 −0.277 3.292 10.992 −0.070 3.283 10.992 2.067 1.320 10.993 0.846 2.526 10.997 1.104 1.514 10.998 −0.355 3.228 10.999 −0.201 3.305 11.000 0.009 2.832 11.000 0.490 1.817 11.002 −0.049 2.901 11.005 1.790 1.676 11.007 −0.307 3.126 11.007 2.099 1.081 11.009 −0.125 2.909 11.009 1.255 1.424 11.009 1.950 1.104 11.012 0.560 1.744 11.013 0.125 3.168 11.014 1.363 2.122 11.015 −0.215 3.160 11.016 −0.111 3.299 11.016 0.711 1.654 11.017 0.997 2.436 11.018 −0.258 3.022 11.019 0.292 3.024 11.020 0.863 1.563 11.021 1.407 1.334 11.022 0.012 3.256 11.024 0.543 1.705 11.025 −0.126 3.203 11.028 1.014 1.473 11.028 −0.153 3.028 11.033 0.105 2.638 11.037 −0.020 3.269 11.037 0.622 1.612 11.037 1.558 1.244 11.037 0.061 2.732 11.038 0.459 2.883 11.038 0.168 2.504 11.039 1.166 1.383 11.039 −0.064 3.070 11.039 0.589 1.608 11.040 1.238 2.391 11.119 0.186 2.543 11.120 1.210 0.597 11.121 0.400 2.320 11.121 0.735 2.696 11.121 2.218 1.233 11.122 1.772 1.023 11.123 1.442 1.030 11.123 0.741 0.900 11.123 1.264 0.946 11.123 1.361 0.142 11.125 0.230 2.376 11.126 0.720 1.176 11.126 2.254 0.926 11.126 0.819 0.735 11.127 2.343 0.968 11.127 0.391 2.802 11.127 0.248 2.410 11.128 0.782 1.043 11.128 0.462 2.187 11.128 1.404 0.072 11.128 1.335 0.332 11.129 0.908 0.545 11.130 1.237 0.771 11.131 0.845 0.911 11.132 0.993 0.365 11.133 1.024 2.614 11.133 1.088 0.164 11.134 0.907 0.778 11.135 1.166 −0.002 11.135 0.480 2.844 11.135 0.524 2.055 11.135 0.306 2.213 11.136 0.310 2.278 11.136 0.453 2.669 11.136 0.809 1.218 11.136 0.969 0.646 11.137 1.031 0.513 11.139 1.683 0.982 11.140 0.871 1.085 11.140 1.094 0.381 11.141 0.587 1.923 11.142 1.156 0.248 11.143 1.468 0.166 11.143 1.361 0.507 11.143 0.516 2.537 11.143 1.218 0.116 11.143 1.025 2.674 11.208 2.557 0.748 11.209 1.867 0.100 11.211 1.973 −0.120 11.211 1.388 0.684 11.212 1.816 0.237 11.212 2.111 −0.346 11.213 1.718 −0.041 11.213 1.513 0.419 11.214 1.104 1.521 11.216 2.432 1.013 11.216 1.870 0.587 11.216 1.700 0.021 11.216 1.638 0.154 11.217 0.933 2.649 11.218 1.693 2.122 11.219 1.006 1.961 11.220 2.061 −0.188 11.221 2.137 0.713 11.221 1.843 0.412 11.222 2.048 0.671 11.226 1.203 2.701 11.227 1.120 2.737 11.228 1.291 1.124 11.228 2.378 0.664 11.230 1.130 1.696 11.232 1.416 2.478 11.232 1.415 0.859 11.232 2.142 −0.251 11.234 2.030 0.015 11.235 1.540 0.594 11.235 1.968 0.148 11.235 1.033 2.136 11.237 2.628 0.702 11.237 1.911 −0.191 11.237 2.126 −0.357 11.237 2.619 0.616 11.238 1.665 0.329 11.239 1.851 −0.069 11.239 0.935 2.576 11.240 2.021 0.497 11.241 1.255 1.431 11.242 1.114 2.734 11.245 1.994 0.322 11.246 1.317 1.299 11.247 2.159 −0.174 11.247 0.997 2.443 11.248 2.583 0.926 11.326 1.834 0.897 11.326 2.428 0.444 11.326 1.994 0.325 11.327 1.389 2.307 11.327 1.292 2.746 11.328 1.871 2.210 11.328 1.305 3.447 11.329 1.358 3.587 11.330 1.897 0.765 11.331 1.246 3.146 11.331 2.696 0.446 11.333 1.256 3.054 11.335 1.737 1.337 11.335 1.497 3.005 11.338 1.514 2.042 11.338 1.328 3.567 11.342 1.416 2.482 11.342 1.576 1.909 11.342 1.319 2.921 11.343 1.746 2.475 11.344 2.582 0.458 11.344 1.861 1.072 11.344 1.281 3.328 11.345 2.922 0.439 11.347 2.277 0.317 11.348 1.283 3.229 11.348 2.521 1.059 11.349 1.622 2.740 11.350 1.701 1.645 11.350 2.208 0.103 11.351 1.524 3.180 11.352 2.048 0.675 11.352 2.860 0.571 11.353 2.361 0.407 11.353 1.763 1.512 11.354 1.541 2.217 11.354 2.833 0.397 11.355 1.345 3.096 11.357 1.443 2.657 11.357 1.319 3.525 11.359 1.498 3.502 11.359 1.310 3.404 11.361 2.247 0.243 11.362 2.146 0.236 11.362 1.888 1.247 11.363 2.718 0.437 11.365 1.800 2.828 11.446 3.011 0.484 11.448 3.079 0.262 11.448 2.201 2.207 11.448 2.245 1.418 11.451 1.981 3.110 11.452 2.023 2.123 11.453 2.263 2.074 11.453 3.111 0.304 11.454 3.004 0.276 11.455 2.370 1.153 11.456 2.145 2.530 11.456 2.994 0.308 11.457 2.494 0.888 11.459 1.925 2.563 11.459 2.045 2.972 11.459 2.619 0.623 11.460 2.949 0.617 11.461 1.827 3.003 11.461 2.388 1.810 11.461 2.147 1.858 11.463 2.681 0.491 11.463 1.773 3.337 11.464 2.110 2.835 11.466 2.255 2.295 11.466 2.513 1.545 11.466 1.792 3.310 11.467 2.887 0.750 11.469 2.301 2.199 11.470 2.637 1.280 11.470 2.272 1.593 11.470 2.049 2.298 11.470 2.286 2.135 11.471 2.824 0.882 11.472 2.762 1.015 11.472 2.175 2.698 11.472 2.833 0.401 11.473 1.952 2.738 11.475 2.396 1.328 11.475 2.239 2.561 11.478 2.521 1.063 11.479 3.077 0.262 11.479 2.174 2.033 11.480 2.646 0.798 11.481 1.916 3.045 11.483 2.770 0.533 11.483 3.110 0.299 11.483 1.674 1.453 10.816 0.524 2.045 10.816 1.763 1.495 10.831 1.336 1.942 10.841 0.119 2.601 10.842 0.240 2.344 10.846 1.434 1.503 10.850 0.386 2.034 10.850 0.353 2.105 10.850 0.516 2.528 10.853 0.819 2.347 10.853 0.667 2.437 10.854 0.676 1.955 10.855 1.585 1.412 10.855 0.364 2.618 10.856 1.782 1.330 10.857 1.282 1.593 10.858 1.826 1.364 10.859 0.123 2.667 10.862 0.827 1.865 10.864 0.970 2.256 10.864 1.130 1.684 10.865 0.979 1.775 10.868 1.737 1.322 10.871 0.213 2.709 10.874 0.082 2.682 10.875 0.188 2.457 10.875 0.311 2.196 10.876 1.487 1.853 10.882 1.122 2.166 10.886 1.915 1.407 10.887 0.435 2.005 10.890 0.049 2.754 10.900 0.061 2.801 10.906 1.888 1.233 10.909 0.302 2.753 10.911 0.147 2.544 10.912 0.605 2.572 10.913 0.453 2.662 10.914 1.977 1.275 10.917 0.150 2.843 10.917 0.756 2.481 10.920 0.011 2.827 10.921 1.639 1.764 10.932 0.587 1.916 10.933 1.957 1.197 10.933 0.908 2.391 10.936 0.774 1.522 11.042 2.191 1.056 11.043 −0.224 2.951 11.044 0.608 2.759 11.044 −0.037 3.245 11.045 0.202 3.106 11.046 0.225 2.383 11.046 0.618 1.547 11.048 0.925 1.432 11.049 0.291 2.243 11.049 1.710 1.153 11.051 0.684 1.480 11.055 0.026 3.113 11.055 1.317 1.293 11.055 1.514 2.033 11.056 −0.196 2.890 11.056 0.642 1.477 11.056 0.358 2.100 11.056 0.351 2.980 11.059 0.639 1.422 11.061 0.836 1.390 11.061 0.557 1.290 11.062 2.102 1.015 11.063 0.625 1.381 11.063 −0.128 2.912 11.064 0.421 1.966 11.064 0.143 3.150 11.066 0.747 1.348 11.067 0.088 2.981 11.068 0.764 2.680 11.068 0.681 1.026 11.068 −0.001 2.939 11.068 0.679 1.266 11.070 0.987 1.300 11.071 1.861 1.063 11.071 0.935 2.570 11.072 1.300 2.256 11.072 0.789 0.796 11.073 0.115 3.155 11.073 0.731 1.156 11.075 1.469 1.203 11.075 −0.044 2.900 11.076 0.809 1.216 11.078 0.888 0.586 11.078 0.791 1.029 11.079 0.497 1.806 11.079 0.523 2.834 11.080 0.934 0.953 11.143 0.373 2.146 11.144 1.415 0.856 11.144 0.747 1.351 11.144 0.378 2.062 11.145 1.594 0.940 11.146 1.286 0.035 11.147 1.389 2.301 11.147 0.676 1.965 11.148 1.924 0.933 11.148 1.524 0.109 11.149 1.524 0.109 11.149 1.058 0.688 11.149 1.481 0.253 11.149 0.578 2.405 11.150 0.649 1.790 11.150 0.836 1.393 11.150 2.164 0.885 11.150 0.435 2.014 11.152 0.658 1.309 11.153 1.388 0.682 11.153 0.584 1.235 11.153 1.183 0.423 11.153 0.445 1.919 11.154 1.308 0.158 11.155 0.774 1.526 11.155 0.711 1.658 11.155 2.405 0.837 11.156 0.640 2.272 11.156 0.961 1.128 11.157 0.543 2.712 11.158 0.497 1.881 11.160 1.556 0.203 11.160 0.509 1.783 11.160 0.886 2.661 11.160 0.800 1.700 11.161 0.557 1.293 11.161 0.644 2.722 11.161 0.703 2.140 11.163 1.085 0.863 11.164 1.406 0.072 11.165 0.607 1.358 11.165 0.560 1.749 11.166 1.513 0.417 11.166 0.571 1.650 11.166 1.834 0.892 11.166 0.684 1.484 11.167 1.157 1.871 11.249 2.289 0.623 11.249 1.036 2.670 11.250 2.370 1.147 11.251 1.969 1.767 11.252 1.442 1.034 11.253 1.060 2.311 11.254 2.200 0.581 11.254 1.567 0.769 11.256 2.530 0.575 11.256 2.119 0.058 11.257 2.065 −0.291 11.257 1.691 0.504 11.258 1.282 1.606 11.259 1.568 2.388 11.260 1.816 0.239 11.260 2.003 −0.159 11.260 2.105 −0.341 11.261 1.024 2.618 11.262 1.292 2.744 11.263 1.176 2.839 11.263 1.941 −0.026 11.264 2.181 −0.075 11.265 1.844 2.033 11.265 1.184 2.046 11.265 2.710 0.566 11.266 2.173 0.407 11.266 1.229 2.877 11.266 1.407 1.341 11.267 2.146 0.233 11.269 2.708 0.659 11.273 1.531 1.077 11.273 1.120 2.733 11.275 1.309 1.781 11.276 2.262 0.449 11.276 2.127 −0.234 11.276 2.440 0.533 11.276 2.156 −0.189 11.278 2.351 0.492 11.281 1.718 0.679 11.282 1.843 0.414 11.282 1.211 2.221 11.283 1.434 1.517 11.284 1.113 2.661 11.284 2.208 0.101 11.285 2.646 0.792 11.285 2.681 0.485 11.285 1.564 3.319 11.367 1.649 2.916 11.368 2.493 0.447 11.369 1.728 1.820 11.369 1.372 3.271 11.370 2.013 0.983 11.370 1.568 2.392 11.371 2.137 0.718 11.372 1.470 2.832 11.372 2.200 0.585 11.373 2.023 2.120 11.373 2.903 0.354 11.373 2.396 1.325 11.375 2.147 1.855 11.377 1.348 3.596 11.378 1.898 2.386 11.379 1.773 2.651 11.380 2.973 0.421 11.381 1.915 1.423 11.381 2.272 1.591 11.382 1.693 2.127 11.382 1.675 3.091 11.382 2.173 0.411 11.383 1.399 3.446 11.384 2.603 0.457 11.385 1.595 2.567 11.386 1.497 3.007 11.387 1.755 1.995 11.387 2.310 0.371 11.387 1.637 3.417 11.388 2.040 1.158 11.389 2.797 0.705 11.389 2.235 0.278 11.390 2.984 0.307 11.391 2.708 0.441 11.393 2.164 0.893 11.393 2.289 0.628 11.396 1.880 1.730 11.396 1.800 2.826 11.397 2.289 0.628 11.398 2.407 0.433 11.398 1.719 2.302 11.398 1.942 1.598 11.400 1.524 3.182 11.401 1.622 2.742 11.401 1.488 3.489 11.406 2.262 0.454 11.406 2.304 2.423 11.484 2.076 2.473 11.487 3.002 0.568 11.488 2.299 1.769 11.489 2.909 0.763 11.489 2.368 2.286 11.490 3.066 0.431 11.491 1.915 3.250 11.492 2.423 1.504 11.495 2.984 0.311 11.496 2.041 2.781 11.497 2.201 2.208 11.498 2.548 1.239 11.499 1.980 3.113 11.500 2.673 0.974 11.502 2.263 2.076 11.502 2.922 0.444 11.504 2.797 0.709 11.504 2.044 2.976 11.508 2.044 2.976 11.508 2.165 2.516 11.509 2.388 1.811 11.511 2.109 2.840 11.515 2.109 2.840 11.515 3.072 0.266 11.516 2.513 1.546 11.517 2.290 2.251 11.520 2.637 1.281 11.521 2.173 2.703 11.522 2.173 2.703 11.522 2.762 1.016 11.524 3.011 0.486 11.526 2.887 0.751 11.526 2.237 2.566 11.528 2.302 2.429 11.534 2.366 2.292 11.539 2.366 2.292 11.539 −0.037 2.890 10.938 0.738 1.826 10.939 −0.001 2.935 10.939 0.890 1.735 10.940 1.041 1.645 10.942 1.344 1.464 10.943 1.496 1.373 10.944 1.193 1.554 10.945 −0.067 2.908 10.946 0.416 1.974 10.947 −0.362 3.240 10.948 0.240 2.886 10.948 0.088 2.977 10.948 0.100 2.645 10.951 1.647 1.283 10.952 1.425 1.987 10.952 −0.098 2.914 10.953 0.216 2.399 10.956 −0.322 3.156 10.957 1.060 2.301 10.957 −0.259 3.256 10.959 −0.130 2.983 10.960 −0.064 3.068 10.960 0.372 2.068 10.960 0.391 2.796 10.961 −0.271 3.282 10.961 −0.220 3.173 10.963 −0.170 3.067 10.963 −0.275 3.057 10.968 2.040 1.144 10.970 −0.126 3.201 10.970 0.063 2.725 10.970 0.026 3.110 10.971 −0.372 3.263 10.971 0.275 2.274 10.973 0.439 1.927 10.973 1.799 1.193 10.974 0.177 3.020 10.975 −0.207 3.299 10.975 0.543 2.706 10.975 −0.228 2.957 10.976 −0.196 2.888 10.979 0.497 1.876 10.982 1.211 2.212 10.984 0.649 1.785 10.985 0.694 2.616 10.985 −0.037 3.243 10.986 0.859 0.884 11.081 2.227 0.981 11.082 2.280 1.099 11.082 0.150 2.849 11.083 1.139 1.210 11.084 0.946 0.699 11.084 1.006 0.571 11.086 1.004 0.339 11.086 0.010 2.834 11.086 0.177 3.023 11.086 0.871 1.084 11.086 1.067 0.442 11.087 1.126 0.315 11.089 0.961 1.126 11.090 1.092 0.154 11.092 0.061 2.807 11.093 0.934 0.951 11.093 1.086 2.480 11.094 1.165 −0.002 11.095 0.240 2.891 11.096 0.213 2.717 11.096 0.577 1.635 11.097 1.620 1.113 11.098 0.304 3.007 11.099 1.182 0.090 11.100 0.074 2.705 11.100 1.058 0.687 11.100 1.291 1.120 11.102 1.942 1.588 11.102 2.013 0.974 11.103 1.112 1.036 11.105 0.275 2.584 11.107 1.232 0.281 11.108 0.123 2.675 11.109 0.639 1.498 11.109 1.183 0.422 11.109 1.259 0.120 11.110 1.285 0.035 11.110 1.085 0.861 11.111 0.337 2.452 11.114 1.666 1.944 11.115 0.625 1.383 11.115 0.148 2.549 11.115 1.531 1.071 11.115 0.892 2.656 11.117 0.329 2.934 11.118 0.668 1.056 11.119 1.567 0.766 11.167 1.210 0.598 11.168 0.640 1.431 11.170 0.925 1.435 11.171 0.622 1.617 11.171 0.634 1.516 11.171 1.335 0.333 11.171 1.745 0.850 11.172 1.719 −0.043 11.172 1.666 0.118 11.174 2.075 0.844 11.175 0.987 1.303 11.175 1.540 0.592 11.175 0.827 1.875 11.176 2.316 0.795 11.180 1.541 2.211 11.180 1.817 1.856 11.181 1.028 2.672 11.182 1.112 1.038 11.183 1.763 0.043 11.186 1.237 0.773 11.187 0.694 2.622 11.188 1.524 0.109 11.188 0.952 1.611 11.188 1.665 0.327 11.189 1.361 0.508 11.190 1.718 0.676 11.191 0.854 2.050 11.192 1.014 1.478 11.193 1.986 0.802 11.193 1.486 0.243 11.193 1.548 0.111 11.194 1.915 −0.194 11.194 0.783 2.665 11.194 0.756 2.490 11.195 2.494 0.880 11.196 2.467 0.705 11.198 1.897 0.761 11.199 1.691 0.502 11.199 1.869 −0.039 11.199 0.819 2.358 11.201 1.139 1.213 11.202 2.093 1.501 11.202 2.227 0.754 11.204 0.979 1.786 11.204 0.881 2.225 11.208 1.264 0.949 11.208 1.202 2.951 11.285 1.256 3.052 11.285 2.770 0.527 11.286 2.092 −0.116 11.286 1.443 2.654 11.288 2.266 0.357 11.288 1.558 1.252 11.290 2.235 0.275 11.291 1.719 2.299 11.291 1.319 2.920 11.292 1.216 3.018 11.293 1.336 1.956 11.293 2.202 0.006 11.296 1.968 0.150 11.297 2.595 0.480 11.297 1.683 0.987 11.298 1.238 2.396 11.299 1.283 3.227 11.299 2.368 0.438 11.299 2.245 1.413 11.300 1.183 2.858 11.300 2.181 −0.074 11.301 1.460 1.692 11.302 2.478 0.466 11.302 1.234 3.110 11.302 1.345 3.095 11.307 1.870 0.590 11.308 1.208 2.979 11.309 1.585 1.427 11.309 1.309 3.355 11.310 1.363 2.132 11.310 2.316 0.388 11.311 2.761 0.449 11.311 1.255 3.217 11.313 1.265 2.571 11.314 1.595 2.565 11.314 1.710 1.162 11.316 2.230 0.143 11.318 1.332 3.461 11.320 1.996 1.944 11.320 1.278 3.325 11.320 1.229 2.879 11.321 2.120 1.679 11.321 1.470 2.830 11.321 1.372 3.270 11.321 2.021 0.499 11.323 2.119 0.060 11.324 2.991 0.440 11.406 1.490 3.509 11.407 1.490 3.509 11.407 2.067 1.333 11.408 1.925 2.561 11.410 2.735 0.838 11.411 3.067 0.313 11.411 1.827 3.001 11.412 2.191 1.068 11.413 2.316 0.803 11.414 3.080 0.266 11.414 1.551 3.357 11.415 1.746 2.477 11.415 1.906 1.905 11.415 1.776 3.332 11.416 2.830 0.383 11.416 1.649 2.917 11.416 2.049 2.296 11.417 2.511 0.455 11.417 2.174 2.031 11.420 2.673 0.971 11.423 2.614 0.460 11.424 1.952 2.736 11.426 1.871 2.213 11.426 2.093 1.508 11.426 1.870 3.113 11.427 2.299 1.767 11.427 2.440 0.538 11.428 1.773 2.652 11.430 1.675 3.092 11.431 2.548 1.237 11.432 2.423 1.502 11.432 2.218 1.243 11.432 2.343 0.978 11.435 1.632 3.423 11.436 1.996 1.948 11.436 1.640 3.399 11.437 2.076 2.472 11.437 2.708 0.446 11.437 2.467 0.713 11.438 2.917 0.330 11.438 3.074 0.351 11.440 1.898 2.388 11.443 2.016 2.804 11.443 1.916 3.247 11.444 2.120 1.683 11.445 1.702 3.267 11.445

It will also be appreciated that the shroud core disclosed in the above Table I may be scaled up or down geometrically for use in other similar turbine designs. Consequently, the coordinate values set forth in Table I may be scaled upwardly or downwardly such that the shroud core profile shape remains unchanged. The scaled version of the coordinates in Table I would be represented by X, Y and Z coordinate values of Table I with X and Y and Z coordinates multiplied or divided by a constant number.

An important term in this disclosure is profile. The profile is the range of the variation between measured points on the shroud core surface and the ideal position listed in Table I. The actual profile on a manufactured blade will be different than those in Table I and the design is robust to this variation meaning that mechanical function is not impaired. As noted above, a + or −0.042 inch profile tolerance is used herein.

Hollow turbine shrouds are advantageous for creating high performance turbine buckets. This specific set of points defines a shroud core for use on a 7FA+e stage 2 bucket and, particularly when coupled with a prescribed shroud tip external profile, optimizes wall thickness distribution, mechanical load transfer, and heat transfer distribution.

While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims. 

1. An article of manufacture including a bucket airfoil having a hollow tip shroud, said hollow tip shroud having a hollow core having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I, in inches, wherein the shape of the core is defined by the cloud of points listed which are distributed around each surface of the shroud, and the complete hollow portion of the tip shroud could be constructed by defining smooth sheet surfaces through the listed points.
 2. An article of manufacture according to claim 1, defining a turbine bucket forming part of a second stage of a turbine.
 3. An article of manufacture according to claim 1 wherein said hollow core shape lies in an envelope within +/−0.042 inches in a direction normal to any hollow core surface location.
 4. An article of manufacture according to claim 1, wherein the X, Y and Z distances are scalable as a function of the same constant or number to provide a scaled-up or scaled-down bucket tip shroud.
 5. An article of manufacture including a bucket airfoil having a hollow tip shroud, said hollow tip shroud having a hollow core having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I, in a Cartesian coordinate system having its origin at a point A located 39.600 inches above the cold rotor center line at an intersection of the airfoil mean camber line and the leading-edge airfoil surface, its positive X axis defined by point A and a point B located 39.600 inches above the cold rotor center line at an intersection of the airfoil mean camber line and the trailing-edge airfoil surface, its positive X-Z plane defined by points A, B, and a point C located 49.862 inches above the cold rotor center line at an intersection of the airfoil mean camber line and the airfoil trailing-edge surface, and its Y axis defined using right-hand rule methodology, and wherein X, Y and Z are distances in inches, wherein the shape of the core is defined by the cloud of points listed which are distributed around each surface of the shroud, and the complete hollow portion of the tip shroud could be constructed by defining smooth sheet surfaces through the listed points.
 6. An article of manufacture according to claim 5, defining a turbine bucket forming part of a second stage of a turbine.
 7. An article of manufacture according to claim 5, wherein said hollow core shape lies in an envelope within +/−0.042 inches in a direction normal to any hollow core surface location.
 8. An article of manufacture according to claim 5, wherein the X, Y and Z distances are scalable as a function of the same constant or number to provide a scaled-up or scaled-down bucket tip shroud.
 9. An article of manufacture comprising a turbine wheel having a plurality of buckets, each of said buckets including an airfoil and a hollow tip shroud, said hollow tip shroud having a hollow core having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I, in inches, wherein the shape of the core is defined by the cloud of points listed which are distributed around each surface of the shroud, and the complete hollow portion of the tip shroud could be constructed by defining smooth sheet surfaces through the listed points.
 10. An article of manufacture according to claim 9, defining a gas turbine and wherein the turbine wheel comprises a second stage of the turbine.
 11. An article of manufacture according to claim 9, wherein said Cartesian coordinate values of X, Y and Z set forth in Table I are in a Cartesian coordinate system having its origin at a point A located 39.600 inches above the cold rotor center line at an intersection of the airfoil mean camber line and the leading-edge airfoil surface, its positive X axis defined by point A and a point B located 39.600 inches above the cold rotor center line at an intersection of the airfoil mean camber line and the trailing-edge airfoil surface, its positive X-Z plane defined by points A, B, and a point C located 49.862 inches above the cold rotor center line at an intersection of the airfoil mean camber line and the airfoil trailing-edge surface, and its Y axis defined using right-hand rule methodology.
 12. An article of manufacture according to claim 9, wherein the X, Y and Z distances are scalable as a function of the same constant or number to provide a scaled-up or scaled-down bucket tip shroud.
 13. An article of manufacture according to claim 12, wherein the turbine wheel comprises a second stage of the turbine.
 14. An article of manufacture according to claim 12, wherein said Cartesian coordinate values of X, Y and Z set forth in Table I are in a Cartesian coordinate system having its origin at a point A located 39.600 inches above the cold rotor center line at an intersection of the airfoil mean camber line and the leading-edge airfoil surface, its positive X axis defined by point A and a point B located 39.600 inches above the cold rotor center line at an intersection of the airfoil mean camber line and the trailing-edge airfoil surface, its positive X-Z plane defined by points A, B, and a point C located 49.862 inches above the cold rotor center line at an intersection of the airfoil mean camber line and the airfoil trailing-edge surface, and its Y axis defined using right-hand rule methodology.
 15. An article of manufacture according to claim 12, said hollow core shape lying in an envelope within +/−0.042 inches in a direction normal to any hollow core surface location. 